Straight Lines

For what values of x, the area of the triangle formed by the points (5,-1), (x,4) and (6,3) is 5.5 sq. units ?

Two vertices of a triangle are (1,3) and (4,-5) and its centroid is (7,2). Find its third vertex.

In what ratio does the point (3,-2) divide the line segment joining the points (1,4) and (-3,16) ?

In what ratio is the line segment joining the points A (2,-3) and B (5,6) is divided by x-axis ? Also find the coordinate of the point of division.

Two points A(3, 4) and B(5, - 2) are given, find the point P such that PA = PB and area of AABP = 20.

Find the slope of each of the lines passing through the points.
(i) A (3,2), B(- 1,6) (ii) P(0,2), Q (1,5)
(iii) P(-1,7), Q(0,3) (iv) R (a2, b), S (b2 a).